We present a novel state feedback design method for perturbed discrete-time switched linear systems. The method aims at achieving (a) closed-loop stability under arbitrary switching and (b) minimisation of ultimate bounds for specific state components. Objective (a) is achieved by computing state feedback matrices so that the closed-loop A matrices generate a solvable Lie algebra (i.e. admit si...

The module of splines on a polyhedral complex can be viewed as the syzygy module of its dual graph with edges weighted by powers of linear forms. When the assignment of linear forms to edges meets certain conditions, we can decompose the graph into disjoint cycles without changing the isomorphism class of the syzygy module. Thus we can use this decomposition to compute the homological dimension...

In this paper, the problem of determining the interval hull (IH) solution x∗ to a linear interval parameter system A(p)x = b(p), p ∈ p is revisited. A new iterative method for computing x∗ is suggested, which is based on individually finding each interval component xk of x ∗. Each component xk = [x ∗ k, x ∗ k] is in turn found by separately determining the lower endpoint xk and upper end-point ...

A bimonotone linear inequality is a linear inequality with at most two nonzero coefficients that are of opposite signs (if both different from zero). A linear inequality defines a halfspace that is a sublattice of Rn (a subset closed with respect to componentwise maximum and minimum) if and only if it is bimonotone. Veinott has shown that a polyhedron is a sublattice if and only if it can be de...

We count subrings of small index $\mathbb {Z}^n$, where the addition and multiplication are defined componentwise. Let $f_n(k)$ denote number $k$. For any $n$, we give a formula for this quantity all integers $k$ that